Polymeric Materials for Microelectronic Applications - American

Chapter 14

Modeling and Simulation of Chemically Amplified Resist Systems Akinori Hongu, Koji Asakawa, Tohru Ushirogouchi, Hiromitsu Wakabayashi, Satoshi Saito, and Makoto Nakase

Downloaded by RUTGERS UNIV on December 2, 2016 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/bk-1994-0579.ch014

Research and Development Center, Toshiba Corporation 1, Komukai Toshiba-cho, Saiwai-ku, Kawasaki 210, Japan

A novel computer simulation program for chemical amplification resist systems have been created accounting for the diffusions of acid and trapping substance, and the reaction caused by the acid to simulate the post-exposure bake (PEB) process of chemical amplification resist systems. Some reaction rate constants those are needed for the simulation have been estimated by experimental data. The model for the PEB process is that the dissolution inhibitor is decomposed by the acid, the acid and the trapping agent deactivate each other, and the acid and the trapping agent diffuse according to their concentration gradients. The dissolution rate of the resist is assumed to be a function of the amount of the remaining dissolution inhibitor. Resist profiles obtained by simulation have the same tendency with actual resist profiles obtained by experiment. It is confirmed that the model, the algorithm, and the constants used in the simulation system are acceptable for simulating chemical amplification resist systems.

A n u m b e r of models have been c r e a t e d t o u n d e r s t a n d the m e c h a n i s m of n o v o l a c diazoquinone type p o s i t i v e - t o n e photoresist systems a n d c o m p u t e r s i m u l a t i o n p r o g r a m s a r e c o m m e r c i a l l y available today. Several of t h e m have p r o v i d e d successful results. However, few m o d e l i n g o r s i m u l a t i o n studies of c h e m i c a l a m p l i f i c a t i o n resist systems have been reported. Conventional s i m u l a t i o n p r o g r a m s f/Jlor p o s i t i v e - t o n e p h o t o r e s i s t systems derive t h e a m o u n t of p h o t o - i n d u c e d d e s t r u c t i o n of t h e d i s s o l u t i o n i n h i b i t o r (diazoquinone) a c c o r d i n g t o t h e exposure light i n t e n s i t y d i s t r i b u t i o n , and c o n v e r t the c o n c e n t r a t i o n of t h e r e m a i n i n g d i s s o l u t i o n i n h i b i t o r i n t o t h e d i s s o l u t i o n rate. On t h e c o n t r a r y , i n c h e m i c a l a m p l i f i c a t i o n p o s i t i v e - t o n e r e s i s t systems, t h e r e i s 0097-6156/94/0579-0176$08.00/0 © 1994 American Chemical Society

Ito et al.; Polymeric Materials for Microelectronic Applications ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

14.

HONGU ET AL.

177 Modeling of Chemically Amplified Resist Systems


another important factor, such as acid diffusion during post-exposure bake (PEB), since the amount of dissolution inhibitor decomposition is determined by the degree of the acid catalyzed reaction. This factor is intrinsically important for chemical amplification resist systems. Furthermore, if any basic substance exists in the resist, or if such a substance enters the resist from the atmosphere via the resist surface, the acid may be trapped and deactivated by the basic substance. In such a system, the developing rate of the resist film after PEB depends on the acid diffusion, the dissolution inhibitor destruction caused by the acid, and the acid trapping by the basic substance, whereas the exposed UV light intensity distribution is only a factor that defines the initial concentration of the acid. Model and Algorithm The model and the algorithm reported here account for the diffusions of the acid and the trapping substance, and the reaction caused by the acid to simulate the PEB process of chemical amplification resist systems. The model can be written in the form of differential equations of the concentrations of the resist components which affect the reactions, accounting for their mutual reaction, self reaction, diffusion, and trapping. Exposure. The model for the exposure process is that the acid generation rate is proportional to the exposed light intensity. Those can be written as follows: - 3CpAG(r,t)/dt

= φ · ε PAG-ln(10)-I(r)- A/(h-c)-CpAc(r,t),

(1)

where CPAc(r,t) is the concentration of the photo acid generator (PAG) at position vector r and exposure time t, Φ is the quantum yield of acid generation, ε PAG is the molar extinction coefficient of the PAG, I(r) is the intensity of the exposed light intensity, λ is the wavelength of the exposed light, h is Planck's constant, and c is the light velocity. This differential equation has a solution, CpAc(r.t)

= CpAG(r,0)-exp(- φ · ε PAG-ln(10)-I(r)- A/(h-c) -t).

(2)

The authors used this equation to calculate the concentration of the PAG after the exposure. The concentration of acid Cacid after exposure is given by Cacid(r.t)

= Cacid(r,0)+jCpAG(r,0)-CpAG(r,t)|.

(3)

The distribution of the exposed light intensity, l(r), was calculated according to a conventional method (2-4) PEB. The model for the PEB process is that the dissolution inhibitor is decomposed by the acid, the acid and the trapping agent deactivate each other,


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POLYMERIC MATERIALS FOR MICROELECTRONIC APPLICATIONS

and the acid and the trapping agent diffuse according to their concentration gradients. These can be written as follows: 3Cinh(r.t)/at dCacid(r.t)/dt


3Ctrap(r.t)/31

" ki-Cinh(r t)-Cacid(r,t) - k -Cinh(r,t),

^

" k3· Cacid(r.t)· Ctrap(r.t) + Dacid-V Cacid(r,t),

®

= - k3-Cacid(r.t)-Ctrap(r.t) + Dtrap-V Ctrap(r,t),

®

n

=

(

=

2

2

2

where Cinh, Cacid, and Ctrap are the concentrations of the dissolution inhibitor, the acid, and the trapping agent, respectively, η is a constant for the acid concentration exponent, t is the PEB time, k i and k3 are the rate constants of the reaction between the dissolution inhibitor and the acid, and of the reaction of the acid and the trapping agent, respectively, k2 is the rate constant of the self decomposition of the dissolution inhibitor, Dacid and Dtrap are the diffusion coefficients of the acid and the trapping agent, and V is nabla. It should be noted that it has become possible by taking the trapping agent into account to evaluate the effect of basic additives like amine and/or basic impurities diffusing from the atmosphere through the resist surface or from the substrate. The above differential equations were transformed to the following difference equations to carry out simulations on a digital computer system:

Cacid(r, t + Δ t)

= - ki-Cinh(r,t)-Cacid(r,t) -At - k2-Cinh(r,t)-At, = - k3 · Cacid(r.t) · Ctrap(r.t) - A t

(5')

Ctrap(r, t + Δ t)

+ Dacid-V Cacid(r,t)-At, = - ka · Cacid(r.t) · Ctrap(r.t) - A t

(6*)

Cinh(r, t+At)

^

n

2

+ Dtrap-V Ctrap(r,t)-At, 2

where A t is assumed to be a very small time fraction, ρ V of both Cacid and Ctrap is calculated by 2

V C

= jC(x+Ax,y,z) + C(x-Ax,y,z)-2-C(x,y,z)i/(Ax)

2

+ jC(x,y+Ay,z) + C(x,y-Ay,z) -2-C(x,y,z)f/(Ay)

2

^

+ iC(x,y,z+Az) + C(x,y,z-Az) -2-C(x,y,z)f/(Az) ' 2

where x, y, and ζ are the Cartesian coordinates of r. Development. The dissolution rate R ( r ) of the resist is assumed to be a function of the amount of the remaining dissolution inhibitor as follows:


14.

Modeling of Chemically Amplified Resist Systems 179

HONGU ET A L

= fj Cinh(r) I

R(r)

(8)


where Cinh(r) is the amount of the remaining dissolution inhibitor at position vector r after PEB. The rate determining function f is defined from experimental data. The minimum duration time, td(x), which is the time between the start of the development and end point of the dissolution of the resist at the position, x, can be described as follows: td(x)

= minj t(p) |,

t(p)

=

/ R(r)dr. p

where t(p) is the duration time through a pass, p, from the surface to position x, and minj t(p) \ is the minimum value among all t(p)s. Constants To carry out the simulation using the above mentioned model, the quantum yield and the molar extinction coefficient of PAG, the reaction rate constants, the diffusion coefficients, and the dissolution rate function should be known. The KrF excimer resist was used for the measurements of the constants, which consists of poly (4-hydroxystyrene) partially protected with t-butoxycarbonylmethyl group as a base polymer and triphenylsulfonium trifluoromethylsulfonate as a photo acid generator. Quantum Yield of PAG. The quantum yield can be derived from the comparison of the exposure dose and the concentration of the generated acid. The measurements of the concentration of the generated acid was made as follows: The resist was coated on a silicone wafer, exposed to a certain amount of exposure dose, and dissolved into an organic solvent which contains a pH indicator, and the absorbance at 602.5 nm was measured. Ethylcellosolve acetate was used as the solvent, and tetrabromophenol blue was used as the pH indicator. The amount of the generated acid was estimated using a calibration curve between the acid concentration and the absorbance at 602.5 nm. Figure 1 shows the experimental data for acid generation. It is clearly seen in the figure that the generated acid increases with increasing the exposure dose, and r e a c h e s the amount of the i n i t i a l PAG c o n c e n t r a t i o n of


180

POLYMERIC MATERIALS FOR MICROELECTRONIC APPLICATIONS

(

- 0

2 . 7 3 x 1 0 " μ π ι . B y fitting a t h e o r e t i c a l curve, equations 2 a n d 3, t o these e x p e r i m e n t a l data using t h e m e t h o d of least squares t h e q u a n t u m yield was e s t i m a t e d t o be 0.27. That i s , 27% of t h e photon absorbed b y PAG r e s u l t s i n a c i d generation.


Reaction Rate Constant. To d e t e r m i n e the r e a c t i o n r a t e of t h e d e c o m p o s i t i o n of the d i s s o l u t i o n i n h i b i t o r c a t a l y z e d by the a c i d , k i i n equations 4 a n d 4 \ t h e a c t i v a t i o n energy, Ea, of t h e r e a c t i o n was m e a s u r e d as follows: The resist was coated on a s i l i c o n wafer, exposed to a c e r t a i n a m o u n t of exposure dose, and s c r a p e d f r o m the wafer, its weight loss was m e a s u r e d by t h e r m o g r a v i n o m e t r y (TG), and a TG s i m u l a t i o n curve was fitted to t h e m e a s u r e d TG data

(5)

TG s i m u l a t i o n c u r v e is given by t h e following difference equation: W(t)

= W(t+At)x[l-Koexpj-Ea/R-T(t)(At],

(11)

where W is t h e weight, Ko is the d e c o m p o s i t i o n r a t e at the infinite t e m p e r a t u r e , R is t h e gas constant, a n d Τ is t h e absolute t e m p e r a t u r e . F i g u r e 2 shows one e x a m p l e of t h e TG data for both s i m u l a t e d a n d m e a s u r e d . In t h e case of this -19 figure, t h e a c t i v a t i o n energy was e s t i m a t e d to be 1 . 4 5 x 1 0 J. Therefore, t h e a c t i v a t i o n energy should be converted to t h e r e a c t i o n r a t e to m a k e t h e s i m u l a t i o n become easier. The r e a c t i o n rate, k i , a n d t h e exponent, n , as functions of t h e t e m p e r a t u r e c a n be obtained by fitting equation 4 u s i n g t h e m e t h o d of least squares to a series of a c t i v a t i o n energy data f o r various c o n c e n t r a t i o n s of t h e a c i d . As a result, the k i a n d η were e s t i m a t e d to be 32.37

ο n m / s a n d 0.733, respectively. Diffusion Coefficient. It is useful to use t h e r e l a t i o n s h i p t h a t t h e diffusion coefficient is p r o p o r t i o n a l to the square of t h e diffusion range. The P E B t e m p e r a t u r e dependence of the diffusion coefficient of the a c i d c a n be e s t i m a t e d by using t h e P E B t e m p e r a t u r e dependence of t h e diffusion range of t h e a c i d , shown i n Figure 3 (7) The diffusion range for P E B t e m p e r a t u r e of 120 °C was estimated to be 1.76 n m / s e c . Dissolution Rate F u n c t i o n . F i g u r e 4 shows t h e e x p e r i m e n t a l data of t h e dissolution rate as a function of t h e i n h i b i t o r content. The d i s s o l u t i o n r a t e c a n be d e s c r i b e d by t h e following equation:


HONGU ET AL.

Modeling of Chemically Amplified Resist Systems

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Polymeric Materials for Microelectronic Applications - American

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